It's an interesting dream. Thank you for sharing this.

Maybe the symbolism of your T appearing drunk in your dream was to show that she has a softer, more vulnerable side, that for professional reasons, she doesn't discuss with you in therapy as they are to do with her personal life, but none the less we all have a softer more vulnerable side, and it's up to us who we choose to show this side to.

And yes, I agree with what you say - "realizing my T is human too, and no more perfect than anyone else". You do know this logically, but dreams sort of project sometimes what we know on a logical level into a symbol of something (your T being drunk).